On the solvability of a forward nonlocal problem for a nonhomogeneous Boussinesq-type equation
##submission.downloads##
In this paper, we study a direct nonlocal problem for a nonhomogeneous Boussinesq-
type equation in a bounded multidimensional domain. The problem is considered under homoge-
neous boundary conditions and a weighted integral condition involving the time variable. Using
the Fourier method and spectral expansion, we derive an explicit form of the solution. Sufficient
conditions for the existence and uniqueness of the solution are obtained, and the convergence of the
corresponding series is established.
1. Boussinesq J. Theorie des ondes et des remous qui se propagent le long d’un canal rectangulaire horizon-
tal,en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au
fond, J. de Mathematiques Pures et Appliques. Deuxime Serie 17, 55-108 (1872).
2. Berezanskii Yu. M., Expansions in eigenfunctions of self-adjoint operators. Translations of Mathematical
Monographs, Vol.17. (American Mathematical Society, Providence, R.I., 1968). 809 p.
3. Alimov Sh. A., Khalmukhamedov A.R. On a Non-Local Problem for a Boussinesq Type Differen-
tial Equation , ISSN 1995-0802, Lobachevskii Journal of Mathematics, 2022, Vol.43, No. 4, 916-923.
https://doi.org/10.1134/S1995080222070046
4. Yuldashev T.K., Mixed differential equation of a Boussinesq type, Vestnik Volgograd. Gos. Universiteta,
Seriya 1, Matem., Fizika 2 33, 13-26 (2016) (in Russian).
5. Yuldashev T. K. On a nonlocal problem for the nonhomogeneous Boussinesq type integro-differential
equation with degenerate kernel, Uch. Zap. Kazan. Univ., Ser.: Fiz.-Mat. Nauki 159, 88-99 (2017).
6. Yuldashev T. K. Solvability of a boundary value problem for a differential equation of the Boussinesq type
Differential Equation 54, 1384-1393 (2018). https://doi.org/10.1134/S0012266118100099
7. Khalmukhamedov A. R. and Kuchkorov E. I., On the solvability of a nonlocal problem for
a Boussinesq type differential equation, Russ. Math. (Iz. VUZ) 67 (10), 54-62 (2023).
https://doi.org/10.3103/S1066369X23100067
8. Dekhkonov Kh. T., Fayziyev Yu. E., Ashurov R. R. On the non-local Problem for a Boussinesq Type
Equations, ISSN 1995-0802, Lobachevskii Journal of Mathematics, 2024, Vol.45, No. 3, pp. 1023-1031.
https://doi.org/10.1134/s1995080224600808
9. Ashurov R. R. , Fayziev Yu. E., and Khudoykulova M. U. , On a non-local problem for a fractional
differential equation of the Boussinesq type, Bull. Karaganda Univ., Math. Ser. 115 (2), 34-45 (2024).
https://doi.org/10.31489/2024m3/34-45
10. Khalmukhamedov A. R. and Kuchkorov E. I., On the solvability of a nonlocal problem for a Boussinesq
type inhomogeneous differential equation, Lobachevskii Journal of Mathematics, 2026, Vol. 47, No. 4, pp.
Mulkiiyat (c) 2026 «O‘zMU XABARLARI»
Ushbu ish quyidagi litsenziya asosida ruxsatlangan Kreativ Commons Attribution-NonCommercial-ShareAlike 4.0 International litsenziyasi asosida bu ish ruxsatlangan..
.jpg)
.png)
